WASHINGTON — The White House brokered an agreement on Monday with intelligence and law enforcement officials that will allow Republican congressional leaders to view some of the most highly classified information related to the Russia investigation, administration officials said.

For months, a small group of lawmakers close to Mr. Trump have been in a pitched fight with the Justice Department over access to some of its most delicate case files, including documents detailing the scope of the Russia investigation by Robert S. Mueller III, the special counsel.

They have trained their focus most recently on access to documents and information related to a secret informant used by F.B.I. agents to gather information from Trump associates who were overseas during the 2016 presidential campaign. Representative Devin Nunes, Republican of California and the House Intelligence Committee chairman, has threatened to hold Rod J. Rosenstein, the deputy attorney general who is overseeing the Russia inquiry, in contempt of Congress or to try to impeach him if he does not hand over the material.

Until Monday, intelligence and law enforcement officials had strenuously resisted both demands, saying that the information was highly sensitive and that it was not appropriate to turn over the unredacted material to Congress, where they fear it could potentially become public or be used to undermine Mr. Mueller’s inquiry. They raised some of their concerns in a letter and then in a face-to-face meeting two weeks ago with Mr. Nunes.

It was not clear after Monday’s meeting how much of that information will now be shared with lawmakers and in what form, or who it will be shared with and in what venue. Democrats have typically been given the same access as their Republican counterparts to delicate files related to the case, but officials on Capitol Hill said they had been given few firm details on the apparent agreement.

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Christopher A. Wray, the director of the F.B.I., after a meeting on Monday at the White House.CreditCarlos Barria/Reuters

White House officials said they expect the disclosure to happen quickly, most likely before the end of the week.

The agreement was made during a White House meeting on Monday afternoon that included Mr. Trump; Mr. Rosenstein; Christopher A. Wray, the director of the F.B.I.; Dan Coats, the director of national intelligence; and John F. Kelly, the White House chief of staff.

Sarah Huckabee Sanders, the White House press secretary, said in a statement afterward that Mr. Kelly would “immediately set up a meeting with the F.B.I., D.O.J. and D.N.I. together with congressional leaders to review highly classified and other information they have requested.”

One official, who was not authorized to speak publicly about the meeting, said the information is likely to satisfy at least some of the demands for information from Republican lawmakers that have been rejected by the intelligence chiefs.

Republican allies of Mr. Trump on Capitol Hill have accused Mr. Rosenstein of obstructing their efforts at legitimate congressional oversight. Allies of Mr. Nunes sent a letter to Mr. Trump asking him to intervene to force the deputy attorney general to turn over all documents requested by Congress.

One of those allies, Representative Mark Meadows, Republican of North Carolina, applauded the outcome on Monday, lavishing praise on Mr. Trump for interceding on behalf of lawmakers.

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President Trump; John F. Kelly, the White House chief of staff; and Dan Coats, the director of national intelligence.CreditDoug Mills/The New York Times; Susan Walsh/AP; Chip Somodevilla/Getty Images

“Their attempt to circumvent this responsibility will not go unnoticed,” he said, referring to Justice Department officials.

A spokesman for Mr. Nunes did not reply to a request for comment.

Democrats have said the repeated confrontations are naked attempts by Republicans to sully the department’s reputation, to expose key details of its investigation and, ultimately, to provide cover to Mr. Trump.

They immediately raised questions on Monday evening about the White House’s motives, with Senator Chuck Schumer, the Democratic leader, calling the plan “highly irregular and inappropriate” and others warning that Justice Department and intelligence officials might have capitulated to Mr. Trump. Several Democratic congressional officials said they were troubled by Mr. Kelly’s potential role, in particular.

“It’s unclear from the statement whether the chief of staff is going to participate in this meeting or is just going to arrange this meeting,” said Representative Adam B. Schiff of California, the top Democrat on the House Intelligence Committee, who has received the same briefings as Mr. Nunes. “The White House should have no role in accessing investigative materials.”

Justice Department officials have argued that disclosure of the information sought by the lawmakers could have dire consequences.

“Disclosure of responsive information to such requests can risk severe consequences, including potential loss of human lives, damage to relationships with valued international partners, compromise of ongoing criminal investigations, and interference with intelligence activities,” Stephen E. Boyd, an assistant attorney general, wrote in a letter to Mr. Nunes.

At the White House meeting, intelligence officials also discussed with Mr. Trump his weekend demand — made on Twitter — that the Justice Department begin an investigation into whether the intelligence agencies improperly spied on his campaign during the 2016 election.

In the tweet Sunday afternoon, Mr. Trump said he planned to formally demand an inquiry into “whether or not the FBI/DOJ infiltrated or surveilled the Trump Campaign for Political Purposes - and if any such demands or requests were made by people within the Obama Administration!”

F.B.I. agents investigating connections between Mr. Trump’s campaign and Russia did send the informant, an American academic who teaches in Britain, to contact three campaign advisers in 2016, but only after receiving evidence that two of the aides had suspicious contacts linked to Russia. No evidence has emerged that the informant acted improperly, but few details are known about his work.

Within hours of Mr. Trump’s tweet, Mr. Rosenstein issued a statement saying that the Justice Department would request that its inspector general expand an existing inquiry to address the president’s concerns.

The White House sought to take credit for that decision on Monday. In her statement, Ms. Sanders said that “based on the meeting with the president, the Department of Justice has asked the inspector general to expand its current investigation to include any irregularities with the Federal Bureau of Investigation’s or the Department of Justice’s tactics concerning the Trump campaign.”

White House officials declined to explain how the Justice Department’s decision on Sunday about the inspector general could be “based on” a meeting with Mr. Trump on Monday.

A version of this article appears in print on , on Page A14 of the New York edition with the headline: G.O.P. Leaders to See Some Details on Inquiry Into Russian Meddling. Order Reprints | Today’s Paper | Subscribe